Fainting area-weria

Geometry Level 2

Given here is a circle with O as centre and radius=7cm. Find the area of the coloured portion. Give your answer to the nearest integer.


The answer is 14.

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2 solutions

Arpan Ray
Sep 29, 2016

Find the area of circle using the formula of π r πr 2 \frac{2}{} . Then divide it by 4 as the included area is quarter of total. Then find the area of the triangle by using the Pythagoras theorem A A 2 \frac{2}{} + B + B 2 \frac{2}{} = H = H 2 \frac{2}{} and then subtract the answer from the divided area of total circle by 4. The answer will be approximately equal to 14.

Andrew Tawfeek
Dec 5, 2015

You can start this problem of by first calculating the area of the triangle made by the radii and the chord: A = 1 2 b h A = 1 2 ( 7 ) 2 = 24.5 A=\frac { 1 }{ 2 } bh\\ A=\frac { 1 }{ 2 } (7)^{ 2 }=24.5

Now, multiplying the area of the triangle by four is the same as creating a square inscribed in the circle above - this time with four green regions.

To find the area of one green region, we subtract the area of the square from the area of the circle then divide by four.

4 A = ( 24.5 ) ( 4 ) = 98 49 π 98 = 55.938 55.938 / 4 14 4A=(24.5)(4)=98\\ 49\pi -98=55.938\\ 55.938/4\approx 14

Yes it was right, but at the second last statement, you would have multiplied 49 directly by π (22/7). [(49*22/7)-98]/4
=[154-98]/4 =56/4 =14

Arpan Ray - 5 years, 6 months ago

It doesn't say that the angle is 90 degrees.

Brian Wang - 5 years, 6 months ago

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